Layered transition metal dichalcogenide (LTMD) compounds constitute a class of materials with unique and unusual properties based on the extreme degree of anisotropy in their layered crystal structures. LTMDs are formed by stacking sandwiches consisting of a layer of transition metal between two layers of chalcogen. There is strong covalent bonding within the sandwiches but weak (van der Waals') bonding between them. Details of the exact crystal type within this general structure vary and result in some LTMDs being very good lubricants and others being poor lubricants or abrasives. Coincidentally, the electrical properties vary greatly also, ranging from insulators to semiconductors, and finally to metals with evidence of superconductivity in some of the class members. Keywords: Electronic structure; Molybdenum disulfide; Solid lubricants; Tribology; Materials properties; Thin films.